We want to evaluate the expression \(\frac{v^2 + u + w}{w}\) for \(u = -12\), \(v = 10\), and \(w = -11\).
First, calculate \(v^2\): \[ v^2 = 10^2 = 100 \]
Next, substitute \(u\) and \(w\) into the expression \(v^2 + u + w\): \[ v^2 + u + w = 100 + (-12) + (-11) \] \[ = 100 - 12 - 11 \] \[ = 100 - 12 = 88 \] \[ 88 - 11 = 77 \]
Now, we can substitute this result into the entire expression: \[ \frac{v^2 + u + w}{w} = \frac{77}{-11} \] \[ = -7 \]
Thus, the simplified answer is: \[ \boxed{-7} \]